Digital filters have widespread use due to the recent advancement of digital signal processing technology. Applications for digital filters include, for examples, their use in analog-to-digital converter (ADC) and digital-to-analog converter (DAC) systems. With known oversampling techniques, DACs and ADCs can reproduce signals at very high levels of accuracy. Sigma-delta noise shaping is one such technique which enables converters to achieve high signal-to-noise ratios with relatively simple hardware. Digital decimation filters are commonly used in sigma-delta ADC systems to decimate and filter the digital output samples from an oversampling modulator to reduce the high frequency quantization noise component in the signal.
Prior art digital decimation filters, used in multi-bit oversampled ADC systems, suffer from a number of drawbacks. Prior to about 1990, such filters were expensive and difficult to implement due to complex hardware requirements. The filters also consumed a lot of power. Burdensome design constraints existed at the time because it was assumed that the multi-bit data words to be filtered had to be multiplied by multi-bit coefficients at high sampling rates. This assumption necessitated filter hardware such as multiple high speed array multipliers (which are expensive and consume a large amount of area - i.e., "real estate" on an integrated circuit "chip"), among other elements, resulting in the aforementioned drawbacks.
In 1990, P. W. Wong and R. M. Gray, in "FIR Filters with Sigma-Delta Modulation Encoding", IEEE Trans. on Acous., Speech and Signal Proc., Vol. 38, p. 979-990, June 1990, which article is herein incorporated by reference, taught that digital finite impulse response (FIR) filters could be realized with truncated filter coefficients restricted to the set {+1, 0 and -1}. Such FIR filters are easy and inexpensive to implement with simple hardware (which does not include multipliers). Additionally, such filters have frequency response characteristics with good stop-band attenuation (cutoff) near the transition frequency. The frequency response of these filters, however, includes poor stop-band attenuation at frequencies above the transition or cutoff frequency. In particular, at such higher frequencies, the frequency response includes stop-band ripple which increases with increasing frequency (the attenuation substantially decreases with increasing frequency above the transition or cutoff frequency). While inexpensive and easily implementable, the deleterious high frequency characteristics of these filters prevents effective use in certain applications. For example, such a filter is not sufficiently effective at reducing high frequency quantization noise in a multi-bit, high order, oversampled ADC system. Accordingly, a general object of the present invention is to provide a digital filter having acceptable high frequency stop-band attenuation which is relatively simple and inexpensive to implement.